Graviton

Existence from the Newton's law of universal gravitation and the Einstein theory of quanta[edit]

The graviton existence can be naively predicted already without any advanced quantum field theory by rewriting the
Newton's law of universal gravitation as the effect of collisions of hypothetical quantum particles with the positive energy
but transferring as the result of the collision strange negative momentum e.g. particles with the negative inertial mass
causing in nonelastic collisions the reaction opposite than normally i.e. casing the negative pressure
(attraction but not the repulsion). While some elastic collisions may not alter the energy of the gravitons for
example they may really have the positive momentum but the neutrons or protons may act as they were active inside for example
if there where Maxwell's demons inside them bouncing the gravitons momentum rigidly back with infinitely heavy
tennis rockets from the forth dimension before the fully non-elastic absorption.

The gravitational force from the large-source mass M{\displaystyle M} acting on the probe mass m{\displaystyle m} at the distance
r{\displaystyle r} is expressed by the formula

F=GMmr2{\displaystyle F=G{\frac {Mm}{r^{2}}}}

Because the gravity force is decreasing with the position distance as 1/r2{\displaystyle 1/r^{2}} it suggests absorption of the
particles by the mass m{\displaystyle m} from the total flux passing through the surface of the sphere 4πr2{\displaystyle 4\pi r^{2}}.

Writing the probe mass m{\displaystyle m} as

m=ρSλ0{\displaystyle m=\rho S\lambda _{0}}

where S{\displaystyle S} is the section of the probe mass, ρ{\displaystyle \rho } is its density and λ0{\displaystyle \lambda _{0}} is its
length or the length of the free path of the absorbed graviton and assuming that the gravitational mass M{\displaystyle M} is radiatively "evaporating"
very slowly and exponentially according to the Einstein formula emitting gravitons i.e.

M=M0e−γt{\displaystyle M=M_{0}e^{-\gamma t}}

we can write then the gravity law as the absorption of the momentum flux

For example this frequency for the Earth with the mass M0=5.972×1024kg{\displaystyle M_{0}=5.972\times 10^{24}kg} is dN/dt=5.09238×1075{\displaystyle dN/dt=5.09238\times 10^{75}}
gravitons per second. It means that with the weakness of the gravity gravitons have almost zero mass and energy. Of course because the gravitational masses in the Universe seem to remain constant both the ω{\displaystyle \omega } and
γ{\displaystyle \gamma } are here almost immeasurably small. As it is seen according to this theory the gravitation between bodies gradually weakens but it happens however
almost immeasurably slowly. Particularly defining the total cross section for the graviton recapturing as σ{\displaystyle \sigma } such that

if we only estimate γ{\displaystyle \gamma } as the inverse of the current age of the Universe counting from the Big Bang i.e.,
the cross section of the order of its spherical geometric section πa02=2.01062×10−30m2{\displaystyle \pi a_{0}^{2}=2.01062\times 10^{-30}m^{2}}.

If we assume the opposite, that the cross section for the graviton capturing by neutron (or proton) is equal to its "seen"
side surface calculated with the known neutron radius a0{\displaystyle a_{0}} i.e.

This formula expresses the relativistic mass in motion with the velocity equal (the rest mass 0) or smaller than the
speed of light c{\displaystyle c} and is the upper limit of the estimation of the rest mass.
[1][2]

As it is seen this relation is in some sense symmetric if one rewrites it as

If from the symmetry of this formula we interpret b0{\displaystyle b_{0}} also as the geometric radius of the graviton and assume
that the graviton at rest is build from the uniform matter with a density similar to that of the proton or the neutron we obtain
the estimate for the rest mass